Most right thinking couples (or triads or quads, or whatever) set certain hardlines when it comes to outside relationships. I definitely wouldn't suggest the childish "This is your problem not mine, NYAH!" approach. It's still possible to keep both relationship from this, but it will take a lighter hand. Outright refusal of your husband's demands will make him resist more or straight-out divorce you.

Sometimes the exertion of control helps a partner feel like they HAVE control. If your husband feels comfortable that he is your primary, you might notice this problem fix itself. Counseling might help a lot with that, it might not. Being resistant and forcing your husband on his ultimatum, that's definitely not going to help unless you want him to walk away.

Acquiescing to her husband's ultimatum will not fix the issue and is only likely to drive them even further apart. Run this scenario: she cuts all contact with boyfriend. She is sad. Maybe she can't hide her sadness. So he has what he thinks he wants, but still feels rejected. He becomes even more resentful. Say she can hide her sadness. Not being able to be honest, hiding feelings, the marriage becomes a total sham. She withdraws and becomes resentful.

It would be totally understandable if the husband stated that he had tried and could not do poly, so he was bowing out. But he will gain nothing by coercion.